Ch. 17, v. 7: "Uviarto horo miKIRBECHO" - We find the words "uviarta hara" (eradicate the bad) in nine verses, all in the book of Devorim. They are:
1) 13:6, dealing with a false prophet
2) 17:7, dealing with an idol worshipper
3) 17:12, dealing with a rebellious Torah scholar
4) 19:13, dealing with a murderer
5) 19:19, dealing with the type of false witnesses called "eidim zom'mim"
6) 21:21, dealing with a rebellious son
7) 22:22, dealing with adultery of a married woman
8) 22:24, dealing with adultery of a betrothed woman, "arusoh"
9) 24:7, dealing with a kidnapper
By six of these cases the verse says "uviarta hara MIKIRBECHO," and you shall eradicate the bad from WITHIN YOU, and by three cases the verse says, "uviarto horo miYISROEL," from the nation YISROEL. The three cases are: a rebellious Torah scholar (17:12), a murderer (19:13), and adultery of a married woman (22:22). The MESHECH CHOCHMOH explains the change of wording. The word "mikirbecho" does not exclude a non-Jew who complies with the seven Noachide mitzvos, a "ger toshov," since later in our parsha the verse says regarding a "ger toshov," "yeisheiv b'KIR'B'CHO" (23:17). When the verse says "miYISROEL" its intention is to indicate that we are only responsible to eradicate the bad from within the Jewish people. Regarding a murderer or an adulterous person who is a "ger toshov" there is no responsibility for the Jewish court to judge and carry out the punishment. The Jewish court only has the responsibility to see that a proper judicial system exists for the "ger toshov" community. This is clearly stated in the Rambam's Sefer Hamitzvos #226-229 and in hilchos m'lochim 10:11. This is why the verses discussing murder and adultery point out that "you must eradicate the bad from YISROEL." Punishing a "ger toshov" is the responsibility of the "ger toshov" community.
The other sins do not apply to a "ger toshov" as there is no punishment for being a false prophet, nor for being false witnesses called "eidim zom'mim," nor for a rebellious son, nor for adultery of a betrothed woman, an "arusoh," as this status of marriage does not exist by them. Thus, the term MIKIRBECHO can be used, as it cannot be misunderstood to include our dealing with eradicating the bad perpetrated by a "ger toshov."
Regarding the rebellious scholar the term "miYISROEL" is used to teach us that his sin is not an affront only to the court with which he differs, and therefore if they wish they may forgive him his sin, or at least they have the choice to forgo administering the death penalty. The verse tells us that his sin is one that affects the complete nation Yisroel. If he were left unpunished it would fuel others to likewise not accept the final binding authority of the court system, and once unbound, the core of unity of the nation would unravel. The Gemara Sanhedrin 88b states that a husband who warned his wife to not go into seclusion with another man may forego bringing her to the Beis Hamikdosh court to go through the "sotah" ritual. Likewise, the parents of a rebellious son have the option of not bringing him to court, but the high court may not forego punishing a rebellious scholar, "shelo yirbu machlokose b'Yisroel," so as to not proliferate disputes within the nation. This is like the ruling that a king who wishes to forego his honour may not do so (K'subos 17a), as the honor he is accorded is not his own to pass up. It is the honour of the nation as represented in its king. Similarly, administering the prescribed punishment to the rebellious scholar is an act of eradication of the bad from the nation YISROEL.
Ch. 18, v. 18,19: "Novi okim lo'hem ...... komocho, Onochi edrosh mei'imo" - The MESHECH CHOCHMOH explains that although Hashem has guaranteed that He would give the bnei Yisroel a prophet "komocho," like Moshe, nevertheless he will not totally have the capacity of Moshe. (This is actually one of the 13 tenets of faith listed by the Rambam.) When Moshe was faced with the rebellion of Korach and his cohorts, he put his lifetime reputation on the line by saying, "Lo Hashem shlochoni" (Bemidbar 16:29). Hashem responded to his request of "V'im brioh yivro Hashem" (verse 30). However, later prophets, even if faced with such a challenge should not respond as Moshe did. Instead, "Onochi edrosh mei'imo," HaShem promises that He will take up the case.
